by
Kaufmann, Jerome; Schwitters, Karen;

Answer

$\frac{5}{3}x^{\frac{11}{15}}$

Work Step by Step

We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression:
$\frac{5x^{\frac{2}{5}}}{3x^{-\frac{1}{3}}}$
$=\frac{5}{3}\times\frac{x^{\frac{2}{5}}}{x^{-\frac{1}{3}}}$
$=\frac{5}{3}\times x^{\frac{2}{5}+(\frac{1}{3})}$
$=\frac{5}{3}\times x^{\frac{2(3)+1(5)}{15}}$
$=\frac{5}{3}\times x^{\frac{6+5}{15}}$
$=\frac{5}{3}\times x^{\frac{11}{15}}$
$=\frac{5}{3}x^{\frac{11}{15}}$